Asked by Noid
Two angles are supplementary and have measures m<QRS = ( x + 40 ) and m<SRT = x What is the measures of <QRS?
180
70
25
110
180
70
25
110
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Two angles are supplementary if their measures add up to 180 degrees. Given the measures of the angles:
- m<QRS = x + 40
- m<SRT = x
We can set up the equation:
\[
m<QRS + m<SRT = 180
\]
Substituting the expressions for the angles:
\[
(x + 40) + x = 180
\]
Combining like terms:
\[
2x + 40 = 180
\]
Subtracting 40 from both sides:
\[
2x = 140
\]
Dividing by 2:
\[
x = 70
\]
Now, we can find the measure of angle <QRS:
\[
m<QRS = x + 40 = 70 + 40 = 110
\]
Therefore, the measure of <QRS is:
\[
\boxed{110}
\]
- m<QRS = x + 40
- m<SRT = x
We can set up the equation:
\[
m<QRS + m<SRT = 180
\]
Substituting the expressions for the angles:
\[
(x + 40) + x = 180
\]
Combining like terms:
\[
2x + 40 = 180
\]
Subtracting 40 from both sides:
\[
2x = 140
\]
Dividing by 2:
\[
x = 70
\]
Now, we can find the measure of angle <QRS:
\[
m<QRS = x + 40 = 70 + 40 = 110
\]
Therefore, the measure of <QRS is:
\[
\boxed{110}
\]
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